Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion, and shape, and they order multivariate data with respect to their centrality. Dyckerhoff and Mosler (201x) have introduced the class of...

Compared with the broad supply of literature measuring socioeconomic gradients in the distribution of health, only little is know about the life course perspective regarding income related inequalities. This article combines the reowned concentration index approach with semiparametric estimation...

The Gini index and the Gini mean difference of a univariate distribution are extended to measure the disparity of a general d-variate distribution. We propose and investigate two approaches, one based on the distance of the distribution from itself, the other on the volume of a convex set in (d...

A new procedure, called DD-procedure, is developed to solve the problem of classifying d-dimensional objects into q ≥ 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0, 1]q ....

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the violation of restrictions. Such a model turns out to be appropriate for many applications and, principally, for the mean-risk portfolio selection problem. Each...